Direct Calculation of the Spin Stiffness in the $J_1$--$J_2$ Heisenberg Antiferromagnet

Abstract

We calculate the spin stiffness ${\rho }_s$ for the frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a square lattice by exact diagonalizations on finite clusters of up to $36$ sites followed by extrapolations to the thermodynamic limit. For the non-frustrated case, we find that ${\rho }_s=(0.183\pm 0.003)J_1$, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for $0.4\lesssim J_2/J_1\lesssim 0.6$. In this intermediate region, the finite-size scaling works poorly -- an additional sign that their is neither Néel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the Néel-ordered region.

4 pages, uuencoded compressed ps-file (made with uufiles)

References in corpus (1)

• Direct Calculation of Spin-Stiffness for Spin-1/2 Heisenberg Models

Cited by in corpus (54)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• The antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field
• A two-dimensional algorithm of the density matrix renormalization group
• Schwinger-boson approach to quantum spin systems: Gaussian fluctuactions in the "natural" gauge
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Quantum Fluctuations and Excitations in Antiferromagnetic Quasicrystals
• Ground state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S=1/2 XY model
• Magnetism and d-wave superconductivity on the half-filled square lattice with frustration
• Magnetic Structure of the $S=1/2$ Quasi-Two-Dimensional Square-Lattice Heisenberg Antiferromagnet Sr${}_2$CuTeO${}_6$
• Detecting spontaneous symmetry breaking in finite-size spectra of frustrated quantum antiferromagnets
• Random-exchange quantum Heisenberg antiferromagnets on the square lattice
• Supersolid phase transitions for hardcore bosons on a triangular lattice
• Anisotropy-induced ordering in the quantum J1-J2 antiferromagnet
• Ground-State Ordering of the $J_1$--$J_2$ Model on the Simple Cubic and Body-Centered Cubic Lattices
• Modified spin-wave theory with ordering vector optimization II: Spatially anisotropic triangular lattice and $J_1{J}_2{J}_3$ model with Heisenberg interactions
• Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
• Spin liquid versus dimer phases in an anisotropic J1-J2 frustrated square antiferromagnet
• Valence-Bond-Glass State with Singlet Gap in the Spin-1/2 Square-Lattice Random $J_1$-$J_2$ Heisenberg Antiferromagnet Sr${}_2$CuTe${}_{1-x}$W${}_x$O${}_6$
• Square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor regular bonds
• The Ising phase in the J1-J2 Heisenberg Model
• Magnetic properties and Mott transition in the square-lattice Hubbard model with frustration
• Cluster functional renormalization group and absence of a bilinear spin liquid in the $J_1$-$J_2$-Heisenberg model
• Two-dimensional randomly-frustrated spin 1/2 Heisenberg model
• Ordered moment in the anisotropic and frustrated square lattice Heisenberg model
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Strong Suppression of Magnetic Ordering in an S = 1/2 Square-Lattice Heisenberg Antiferromagnet Sr2CuTeO6
• Hydrodynamic relation in 2D Heisenberg antiferromagnet in a field
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
• Role of Frustration and Dimensionality in the Hubbard Model on the Stacked Square Lattice: Variational Cluster Approach
• Theoretical studies of the phase transition in the anisotropic 2-D square spin lattice
• The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment
• Charge and Spin Transport in the One-dimensional Hubbard Model
• Modified Spin Wave Thoery of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet
• Contrasting Magnetic Structures in SrLaCuSbO${}_6$ and SrLaCuNbO${}_6$: Spin-1/2 Quasi-Square-Lattice $J_1-J_2$ Heisenberg Antiferromagnets
• Weakly frustrated two-dimensional Heisenberg antiferromagnets: thermodynamic properties from a non-perturbative approach
• Entanglement in first excited states of some many-body quantum spin systems: indication of quantum phase transition in finite size systems
• Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy
• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction
• Effective action approach to a bi-layer frustrated antiferromagnet
• 2D excitation information by MPS method on infinite helixes
• Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet
• Entanglement of Hard-Core Bosons in Bipartite Lattices
• Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions